%I #20 Apr 25 2024 09:18:47

%S 1,6,44,360,3088,26976,237248,2091648,18456832,162915840,1438198784,

%T 12696741888,112091336704,989587267584,8736489783296,77129433907200,

%U 680931492954112,6011553766047744,53072563389857792,468547255228956672

%N a(n) = ((6 + sqrt(8))^n + (6 - sqrt(8))^n)/2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -28).

%F From _Philippe Deléham_, Nov 13 2008: (Start)

%F a(n) = 12*a(n-1) - 28*a(n-2), a(0)=1, a(1)=6.

%F G.f.: (1-6x)/(1-12x+28x^2).

%F a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2k)*8^(n-k))/6^n. (End)

%F a(n) = 2^n*A083878(n). - _R. J. Mathar_, Feb 04 2021

%t LinearRecurrence[{12,-28},{1,6},30] (* _Harvey P. Dale_, Apr 23 2011 *)

%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((6+r8)^n+(6-r8)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 13 2008

%K nonn,easy

%O 0,2

%A Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008

%E Extended beyond a(6) by _Klaus Brockhaus_, Nov 13 2008